Adding a cover into Calibre does NOT (at that point anyway) embed it into the ebook file. At that point it is simply stored in the Calibre library structure.

It is embeded into the ebook file if you run a conversion.

It is also often added when you use Calibre to send a book to a device/folder/iTunes - but that relies on Calibre being able to find an existing cover that it can replacem and can be file-type dependant. As a general rule it MAY work for epub files (depending how they were created) and is less likely to work for pdf files.

You did not mmention how you are transfering the books to the device. If you are doing it outside calibre then the only way to get it embedded is to run the conversion.

The .opf and .jpg files are not MEANT to be transferred - they are part of Calibre's internal working.

As I said eaerlier the only reasonable reliable way to get a cover embedded in a file is to run a conversion (even if it is epub->epub). However if you do that it is always a good idea to ahve kept another copy of the file outside calibre control in case the conversion has undesireable side-effects on the layout (although this is rare for epub->epub conversions).

Note that there are other manual ways of updating the cover for epub files without running a conversion, but if you are not used to calibre then the conversion is the easiest one to try.